REAL-TIME DYNAMICS OF SOLITON DIFFUSION

We study the nonequilibrium dynamics of solitons in model Hamiltonians for Peierls dimerized quasi-one dimensional conducting polymers and c ommensurate charge-density-wave systems. The real-time equation of mot ion for the collective coordinate of the soliton and the associated La ngevin equation is found in a consistent adiabatic expansion in terms of the ratio of the optical phonon or phason frequency to the soliton mass. The equation of motion for the soliton collective coordinate all ows one to obtain the frequency-dependent soliton conductivity. In low est order we find that although the coefficient of static friction van ishes, there is dynamical dissipation represented by a non-Markovian d issipative kernel associated with two-phonon processes. The correlatio n function of the noise in the quantum Langevin equation and the dissi pative kernel are related by a generalized quantum-fluctuation dissipa tion theorem. To lowest adiabatic order we find that the noise is Gaus sian, additive, and colored. We numerically solve the equations of mot ion in lowest adiabatic order and compare to the Markovian approximati on which is shown to fail both in the phi(4) and the sine-Gordon model s even at high temperatures. [S0163-1829(98)05202-3].